1. State Leibnitz's theorem. If y = (x-1)", then prove that (x-1)y+2+2xy + -n(n-1)y, =0 2. Assuming the validity of expansion, expand log(1+ sin x) by Maclaurin's therom. lim (1+x)-e 3. Evaluate x 0 X 4. Find the asymptotes of the curve: x(x-y)2-3(x-y)+8y=0 5. Find the radius of curvature at any point (r,0) for the curve a = r cos 20 6. Show that: xsin x 1+cos x -dx 4